Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

Abstract

Introduction. In the case of a high level of free-stream turbulence (0.1% < ~t < 5%). the laminarturbulent transitiou occurs without fornmtion of the Tolhnien-Schlichting waves [1]. Instead of them. the growth of low-frequency perturbations of velocity is observed. Flow visualization shows that these 1)erturbations are narrow streaks exteuded in the streamwise direction [2]. It is ~ussu,ned that these streaky structures appear as a resul: ~ 1)enetration of ~x)rtices from the external flow into the boundary layer and their subsequent amplificat~,,a in it. Th~;refore, the solution of the t)rot)lem of recel)tivity of the 1)oundary layer to vortex disturbances is an important component in developing the theory of the laminar-turbulent transition in the case of an elevated level of t'ree-stream turbulence.This problem ha.s been sol~vd only for the particular case of interaction of streamwise vortices with tile boundary layer on a fiat plate [3,4]. This is tile siml)lest case, since tim free-stream vorticity field is not distorted by tile flow near the leading edge. However, such a deformation involves a(htitional amplification of pertltrbations due to the exi)ansion of vortex filaments [5]. Tile gTeatest amI)lification is experienced by I), :, bations whose vortex lines intersect tile lea(ting edge. Hence, these perturbations (and not tile streamwise vortices) should generate the streaky structure most effectively. It is shown in [5] that vorticity perpendicular to the leading edge (or nonuniformity of tile velocity profile in the spanwise (tirectit)tt) can even lead to a local separation of tile boundary layer. The analysis [5] was made for large-scale disturbances of small but finite amplitu(le. Under tim assumt)tions accel)ted, the development of disturbances is actually inviscid, and tile governing influence is exerted by nonlinear effects. However, it follows from the exl)erimental results of XNestin et al. [6] that the transverse size of the streaky structure is small, and viscosity plays a significant role in the development of this structure. In addition, the aml)litude of perturbations observed in [6] is small for manif'estation of strong nonlinear effects. In the I)resent work, the I)robleIn of interaction of a nonuniform flow with the boundary layer is solved under tile folh)wing ~lssumptions: the characteristic size of disturban('es is assumed to be of the order of the 1)oun(lary-layer thickness and the evolution of (listurbances is linear in terms of their amplitude.

Separated flows receptivity for external disturbances

“…As it was shown in paper [2], to describe free-stream perturbations caused by turbulence, the energy, spectral, and scale characteristics of the latter are used [4,5]. In most papers, the effect of the turbulence level on the flow structure is considered, whereas the role of, e.g., free-stream velocity in homogeneities or macroscale of turbulence has not been adequately studied [5][6][7][8][9][10][11][12]. In practice, the isolated influence of the elevated level of turbulence is rarely observed; therefore, combined effects are often studied.…”